Question

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal mono-atomic gas. The amount of heat, extracted from the source in a single cycle is :

• A. $\left(\frac{13}{2}\right)p_0{V}_0$
• B. $p_0{V}_0$
• C. $4p_0{V}_0$
• D. $\left(\frac{11}{2}\right)p_0{V}_0$

Answer 1

The correct option is A $\left(\frac{13}{2}\right)p_0{V}_0$

Heat is extracted from the source, means heat is given to the system (or gas) or $Q$ is positive. This is positive only along the path ABC.

Heat supplied= $Q_{ABC}+W_{ABC}$

$=n{C}_v(T_f-T_i)+\text{area under P-V graph}$

$=n\left(\frac{3}{2}R\right)(T_C-T_A)+2p_0{V}_0$

$=\frac{3}{2}(nR{T}_C-nR{T}_A)+2p_0{V}_0$

$=\frac{3}{2}(p_C{V}_C-p_A{V}_A)+2p_0{V}_0$

$=\frac{3}{2}(4p_0{V}_0-p_0{V}_0)+2p_0{V}_0$

$=\frac{13}{2}\left(p_0{V}_0\right)$

Hence, option $\left(B\right)$ is correct.